Related papers: Turing instabilities on Cartesian product networks
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…
Long after Turing's seminal Reaction-Diffusion (RD) model, the elegance of his fundamental equations alleviated much of the skepticism surrounding pattern formation. Though Turing model is a simplification and an idealization, it is one of…
We introduce diffusively coupled networks where the dynamical system at each vertex is planar Hamiltonian. The problems we address are synchronisation and an analogue of diffusion-driven Turing instability for time-dependent homogeneous…
For delayed reaction-diffusion Schnakenberg systems with Neumann boundary conditions, critical conditions for Turing instability are derived, which are necessary and sufficient. And existence conditions for Turing, Hopf and Turing-Hopf…
Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor…
This paper focuses on the consensus and formation problems of multiagent systems under unknown persistent disturbances. Specifically, we propose a novel method that combines an existing consensus (or formation) algorithm with a new…
Streamer ionization fronts are pulled fronts propagating into a linearly unstable state; the spatial decay of the initial condition of a planar front selects dynamically one specific long time attractor out of a continuous family. A…
A class of systems is considered, where immobile species associated to distinct patches, the nodes of a network, interact both locally and at a long-range, as specified by an (interaction) adjacency matrix. Non local interactions are…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
We study the onset of spatial instabilities in reaction networks where the spatially homogeneous system admits a steady state parameterization. We formulate a sufficient condition -- based on the signs of the constant and leading…
Known by many names and arising in many settings, the forced linear diffusion model is central to the modeling of power and influence within social networks (while also serving as the mechanistic justification for the widely used…
We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing…
Motivated by numerical simulations showing the emergence of either periodic or irregular patterns, we explore a mechanism of pattern formation arising in the processes described by a system of a single reaction-diffusion equation coupled…
This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…
We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…